The German word for “curious”, in the sense of “inquisitive”, is “neugierig”. This wonderful word literally translates as “greedy for something new”. Its corresponding nouns (“curiosity”) are both “Neugier” (f.) and “Neugierde” (f.) (but note that “greed” is only “Gier”):

– “Just out of curiosity, what are you doing?” – “Nur aus Neugier, was machst du?”
– “Er muss seine Neugier befriedigen.” – “He has to satisfy his curiosity.”
– “Langsam werde ich neugierig.” – “I’m slowly getting curious.”

The word “curious” in the sense of “peculiar” or “odd” is “merkwürdig” in German (literally it translates as “noteworthy”, but only “bemerkenswert” is used in this way). The sound-alike “kurios” also means “strange”:

– “Es war ein wirklich merkwürdiger Vorfall.” – “It was a truly odd/curious incident.”
– “Es war eine wirklich bemerkenswerte Leistung.” – “It was a remarkable/noteworthy achievement.”
– “Es ist eine kuriose Sache.” – “It’s a curious/odd thing.”